摘要
Hitczenko[2]证明了不等式 E(sum from i=1 to γ(ζ_i))~γ≤2(γ-1)E(sum from i=1 to γ~2(ζ_i))~γ,1≤γ〈∞,其中(ζ_i)为非负独立随机变量,γ为停时,γ′为停时γ的一个复制品,且与(ζ_i)独立,2(γ-1)是最佳常数,我们证明了,对于非负独立同分布的(ζ_i),2(γ-1)也是最佳常数,从而解决了Hitczenko[2]提出的问题。
Hitczenko [2] studied the following inequalitywhere (ξi) is a sequence of independent non-negative random variables, r is a stopping time, r' is a copy of r independent of the sequence (ξi), and Cr is a constant which does not dependent on (ξi). He obtained that the best possible constant for above inequality is Cr = 2r-1. A question concerning the best possible constant for the above inequality when (ξi) is a sequence of non-negative i.i.d. random variables was raised in Hitczenko [2]. We show here that the constant Cr = 2r-1 is also sharp for sums of non-negative i.i.d. random variables.
出处
《应用概率统计》
CSCD
北大核心
1996年第1期77-80,共4页
Chinese Journal of Applied Probability and Statistics
关键词
不等式
停止和
独立同分布
随机变量
Moment inequality, stopping time, i.i.d. random variables.
